2024/11/22 by Batlle, Carlos, Figueroa-O'Farrill, José, Gomis, Joaquim +1 · 1 citation
#81R10 81T40 (Primary) 17B65 17B69 17B81 (Secondary) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2411.14866
We generalise BMS algebras in three dimensions by the introduction of an arbitrary real parameter λ, recovering the standard algebras (BMS, extended BMS and Weyl-BMS) for λ=-1. We exhibit a realisation of the (centreless) Weyl λ-BMS algebra in terms of the symplectic structure on the space of solutions of the massless Klein-Gordon equation in 2+1, using the eigenstates of the spacetime momentum operator. The quadratic Casimir of the Lorentz algebra plays an essential rôle in the construction. The Weyl λ-BMS algebra admits a three-parameter family of central extensions, resulting in the (centrally extended) Weyl-BMS algebra, which we reformulate in terms of operator product expansions. We construct the BRST complex of a putative Weyl-BMS string and show that the BRST cohomology is isomorphic to the chiral ring of a topologically twisted N=2 superconformal field theory. We also comment on the obstructions to obtaining a conformal BMS Lie algebra -- that is, one that includes in addition the special-conformal generators -- and the need to consider a W-algebra. We then construct the quantum version of this W-algebra in terms of operator product expansions. We show that this W-algebra does not admit a BRST complex.